I keep trying, but I can't get this.

The two solutions of the equation x^2 + bx + 18 = 0 are in the ratio of 3 to 1 for some values of b. What is the largest possible value of b?

Guest Nov 27, 2022

#1**-1 **

Hm.. can you explain further for the 3:1 ratio is it for the variable b or the variable x?

Imcool Nov 27, 2022

#2**-2 **

**I get it now. Okay so first, look at the constant term 18. we need some 2 numbers to be in a 3:1 ratio and multiply to get 18 so**

**\(xy=18\)**

**\(4y=x\)**

**from this system of equations we get**

**\(y = \sqrt{4.5}\)**

**\(x = \sqrt{72}\)**

**these are the 2 solutions the this quadratic.**

**we can express this as**

**\((x - \sqrt{4.5})(x-\sqrt{72}) = 0\)**

**so b is equal to \(\sqrt{4.5} + \sqrt{72}\)**

**hope this helped(i hope this is not wrong)**

Imcool Nov 27, 2022